# coupled

1. ### Approximation method for coupled DEq

I've derived the equations of motion for a double (physical) pendulum. There are two coupled equations and I need to solve them numerically for \alpha (t) and \beta (t). I thought I'd see if anyone would suggest a method: I'm leaning toward a Runge-Kutta solution, but might there be a better...
2. ### Solving a coupled pair of differential equations using matrices

I am asked to find the eigenvalues and eigenvectors of the matrix: A = \left(\begin{array}{cc}5&3\\1&7\end{array}\right) I find them as \lambda_1 = 8 , \lambda_2 = 4 and v_1 = (1,1) , v_2 = (-3,1) The equations I need to solve are: \frac{dx}{dt} = 5x +3 y and \frac{dy}{dt} = x + 7y...
3. ### coupled differential equations

I really have no idea to go about doing question 2, I can't find any information about coupled differential equations that I understand, or any examples to help. Here's question 1 to help with question 2 Thanks in advance for anyone who can offer advice. (Bow)(Bow)
4. ### Coupled differential equations

Anyone know how to solve these equations without using eigenvalues/eigenvectors? Can these be solved using standard integration techniques? dx/dt = 4x+2y dy/dt = -x +y where x and y are functions of t.
5. ### MATLAB 2nd order nonlinear coupled differential eq

Hey Everybody, i have to do a simulation in matlab by simulating the motion of a babyboot. But my problem is that i dont know what to do. This is the link of the excercise i have to do: http://www.stanford.edu/class/me331b/documents/BabybootEOMStudent.pdf Maybe someone could help me and...
6. ### My pair of coupled nonlinear differential equations

Hello every one, In my physics problem, i end up having two coupled second-order nonlinear differential equations where the coupling terms include, the variable, the first derivatives, and also a second derivative coupling. I appreciate any help on how to handle this system before setting it...
7. ### two coupled nonlinear differential equations

Hello every one, In my physics problem, i end up having two coupled second-order nonlinear differential equations where the coupling terms include, the variable, the first derivatives, and also a second derivative coupling. I appreciate any help on how to handle this system before setting it...
8. ### Coupled partial differential equation...how to find a solution?

I have four coupled pde's I need to find solutions to, they are; \hbar \frac{\partial}{\partial t}W_{(x,y,t)} = g_1 \left( sin(\omega t) \frac{\partial}{\partial x} - cos(\omega t) \frac{\partial}{\partial y} \right) \Gamma_{(x,y,t)} +g_2 \left( sin(\omega t) \frac{\partial}{\partial x} -...
9. ### Damped Oscillator equation. Finding Energy and general solution for coupled oscillato

Hi! I can do (a) easily enough but (b) has me totally stumped altogether! I can't seem to figure out how they get it in that form! Also (c) I'm having the same problem. I have two exams tomorrow and this is the first one so im juggling between the two subjects going through the past papers so if...
10. ### Coupled Linear System in matrix form

I want to change this coupled linear system to the form dx/dt=Ax where A is a Matrix. we have dx/dt=3y-4x dy/dt=5y-6x can anyone explain to me how to do it? I have no idea... I think A= (-4 3) (-6 5) am i wrong?
11. ### Inner Product Spaces Coupled with Transformations

Hey, I'm having so much trouble wrapping my head around inner product spaces and transformations. I don't know where to start (see attached in picture). Could anyone help me through part a), so maybe I could make it on to part b and c Any help is greatly apprectiate Thanks in advance
12. ### Coupled Differential Equations

Hey, I've been set a question which i have no idea how to attempt. Please could some one show me some guidance? thanks Question: y'(x) +z(x)= x z'(x) +4y(x)=0 y(0)=1 z(0)=-1
13. ### How to solve coupled optimization problem?

Hi there, I have got a problem of solving coupled optimization problem in real application. For example, The objective function E(a,b) contains two sets of variables need to be optimized: E(x, a) = \frac{1}{2}\bigg(y - W(a)x\bigg)^2; Assume W(a) is a transformation matrix describing...
14. ### finite difference method, coupled wave equations, chickens & eggs

I'm reading a book (Numerical Techniques in Electromagnetics by Sadiku) & just finished the section on finite difference methods. As what I thought would be an easy exercise, I tried to apply what I'd learned to the telegraphers equations that describe the voltage, V(x, t), and current, I(x, t)...
15. ### coupled differential equation

Hi my question is use any appropriate method to find the general solution to the coupled system of ODEs. \dot{y}-y+z=e^{-t} \dot{z}-2z=3e^{-t} i tried to differentiate first equation. but wasn't getting anywhere.
16. ### System of second order linear homogenous differential coupled equations

my question is: what is the general solution of this system of coupled diff. equations: f ''i = Cijfj Cij is a matrix, fj(z) are functions dependent of z. indexes i and j go from 0 to N .
17. ### coupled 1st order ODEs, and initial conditions...

Hi, I'm having some trouble with this problem...if anyone could help me out a bit that'd be great - it's really just one bit of it i don't get. Solve the pair of differential equations: dx/dt = ax dy/dt = ay + bx where a and b are arbitrary constants. All subject to the...
18. ### steady state - coupled ODEs

I have a system of 6 coupled ODEs: W\frac{dl_E}{dt} = -l_E\rho_F + \psi_Ll_B \frac{dl_B}{dt} = \rho_Fl_E - \psi_Ll_B - \chi_Ll_B \frac{dl_I}{dt} = \chi_Ll_B - \omega_Ll_I \sigma\frac{d\rho_F}{dt} = \gamma_{rr}\sigma\rho_I - \chi_0\rho_F - (ml_E\rho_F - m\psi_Ll_B +...
19. ### Coupled mass to matrix problem

Hi, I am new around here. Hope you don't mind me beginning my stay with a question. 1. The Problem Suppose masses m_{1}, m_{2}, m_{3}, m_{4} are located at positions x_{1}, x_{2}, x_{3}, x_{4} in a line and connected by springs with constants k_{12}, k_{23}, k_{34} whose natural lengths of...
20. ### coupled equations

dx/dt - 5x = -3Ae^2t ----> 2x-5x^2 = -3Ae^2t what should i do to get the answer? thx